# Difference between revisions of "Cylindrical coordinates"

From Conservapedia

DavidB4-bot (Talk | contribs) (→top: clean up & uniformity) |
(converted to maths formulae) |
||

Line 1: | Line 1: | ||

− | '''Cylindrical coordinates''' refers to a three-dimensional coordinate system used to describe the location of a point in space based on the distance from the origin in the x-y plane | + | '''Cylindrical coordinates''' refers to a three-dimensional coordinate system used to describe the location of a point in space based on the distance from the origin in the x-y plane <math>r</math>, the angle measured in the x-y plane between the point and the x axis <math>\theta</math>, the distance perpendicular to the x-y plane: <math>(r, \theta. z)</math> |

− | In a sense, cylindrical coordinates are polar coordinates with a third dimension added: (r, | + | In a sense, cylindrical coordinates are polar coordinates with a third dimension added: <math>(r, \theta)</math> correspond to the polar coordinates for <math>(x, y)</math>. This is in contrast to [[spherical coordinates]], where <math>z</math> is replaced by an angle, just like x and y are in polar coordinates. |

The equations converting the parameters are as follows: | The equations converting the parameters are as follows: | ||

− | : | + | :<math>r^2 = x^2 + y^2</math> |

− | :tan | + | :<math>\tan{\theta} = \frac{y}{x}</math> |

− | :x = r | + | :<math>x = r \cos{\theta}</math> |

− | :y = r | + | :<math>y = r \sin{\theta}</math> |

+ | |||

+ | In cylindrical coordinates, the Jacobian is <math>r</math> so that <math>\text{d}x \, \text{d}y \, \text{d}z = r \text{d}r \, \text{d} \theta \, \text{d}z</math>. | ||

[[Category:Mathematics]] | [[Category:Mathematics]] | ||

[[Category:Geometry]] | [[Category:Geometry]] |

## Latest revision as of 14:08, 14 December 2016

**Cylindrical coordinates** refers to a three-dimensional coordinate system used to describe the location of a point in space based on the distance from the origin in the x-y plane , the angle measured in the x-y plane between the point and the x axis , the distance perpendicular to the x-y plane:

In a sense, cylindrical coordinates are polar coordinates with a third dimension added: correspond to the polar coordinates for . This is in contrast to spherical coordinates, where is replaced by an angle, just like x and y are in polar coordinates.

The equations converting the parameters are as follows:

In cylindrical coordinates, the Jacobian is so that .